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      SUBROUTINE <a name="SGGES.1"></a><a href="sgges.f.html#SGGES.1">SGGES</a>( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
     $                  SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR,
     $                  LDVSR, WORK, LWORK, BWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          JOBVSL, JOBVSR, SORT
      INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      LOGICAL            BWORK( * )
      REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
     $                   B( LDB, * ), BETA( * ), VSL( LDVSL, * ),
     $                   VSR( LDVSR, * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Function Arguments ..
</span>      LOGICAL            SELCTG
      EXTERNAL           SELCTG
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="SGGES.27"></a><a href="sgges.f.html#SGGES.1">SGGES</a> computes for a pair of N-by-N real nonsymmetric matrices (A,B),
</span><span class="comment">*</span><span class="comment">  the generalized eigenvalues, the generalized real Schur form (S,T),
</span><span class="comment">*</span><span class="comment">  optionally, the left and/or right matrices of Schur vectors (VSL and
</span><span class="comment">*</span><span class="comment">  VSR). This gives the generalized Schur factorization
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Optionally, it also orders the eigenvalues so that a selected cluster
</span><span class="comment">*</span><span class="comment">  of eigenvalues appears in the leading diagonal blocks of the upper
</span><span class="comment">*</span><span class="comment">  quasi-triangular matrix S and the upper triangular matrix T.The
</span><span class="comment">*</span><span class="comment">  leading columns of VSL and VSR then form an orthonormal basis for the
</span><span class="comment">*</span><span class="comment">  corresponding left and right eigenspaces (deflating subspaces).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  (If only the generalized eigenvalues are needed, use the driver
</span><span class="comment">*</span><span class="comment">  <a name="SGGEV.41"></a><a href="sggev.f.html#SGGEV.1">SGGEV</a> instead, which is faster.)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
</span><span class="comment">*</span><span class="comment">  or a ratio alpha/beta = w, such that  A - w*B is singular.  It is
</span><span class="comment">*</span><span class="comment">  usually represented as the pair (alpha,beta), as there is a
</span><span class="comment">*</span><span class="comment">  reasonable interpretation for beta=0 or both being zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A pair of matrices (S,T) is in generalized real Schur form if T is
</span><span class="comment">*</span><span class="comment">  upper triangular with non-negative diagonal and S is block upper
</span><span class="comment">*</span><span class="comment">  triangular with 1-by-1 and 2-by-2 blocks.  1-by-1 blocks correspond
</span><span class="comment">*</span><span class="comment">  to real generalized eigenvalues, while 2-by-2 blocks of S will be
</span><span class="comment">*</span><span class="comment">  &quot;standardized&quot; by making the corresponding elements of T have the
</span><span class="comment">*</span><span class="comment">  form:
</span><span class="comment">*</span><span class="comment">          [  a  0  ]
</span><span class="comment">*</span><span class="comment">          [  0  b  ]
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  and the pair of corresponding 2-by-2 blocks in S and T will have a
</span><span class="comment">*</span><span class="comment">  complex conjugate pair of generalized eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBVSL  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  do not compute the left Schur vectors;
</span><span class="comment">*</span><span class="comment">          = 'V':  compute the left Schur vectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBVSR  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  do not compute the right Schur vectors;
</span><span class="comment">*</span><span class="comment">          = 'V':  compute the right Schur vectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SORT    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether or not to order the eigenvalues on the
</span><span class="comment">*</span><span class="comment">          diagonal of the generalized Schur form.
</span><span class="comment">*</span><span class="comment">          = 'N':  Eigenvalues are not ordered;
</span><span class="comment">*</span><span class="comment">          = 'S':  Eigenvalues are ordered (see SELCTG);
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SELCTG  (external procedure) LOGICAL FUNCTION of three REAL arguments
</span><span class="comment">*</span><span class="comment">          SELCTG must be declared EXTERNAL in the calling subroutine.
</span><span class="comment">*</span><span class="comment">          If SORT = 'N', SELCTG is not referenced.
</span><span class="comment">*</span><span class="comment">          If SORT = 'S', SELCTG is used to select eigenvalues to sort
</span><span class="comment">*</span><span class="comment">          to the top left of the Schur form.
</span><span class="comment">*</span><span class="comment">          An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if
</span><span class="comment">*</span><span class="comment">          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either
</span><span class="comment">*</span><span class="comment">          one of a complex conjugate pair of eigenvalues is selected,
</span><span class="comment">*</span><span class="comment">          then both complex eigenvalues are selected.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          Note that in the ill-conditioned case, a selected complex
</span><span class="comment">*</span><span class="comment">          eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j),
</span><span class="comment">*</span><span class="comment">          BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2
</span><span class="comment">*</span><span class="comment">          in this case.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrices A, B, VSL, and VSR.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) REAL array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment">          On entry, the first of the pair of matrices.
</span><span class="comment">*</span><span class="comment">          On exit, A has been overwritten by its generalized Schur
</span><span class="comment">*</span><span class="comment">          form S.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) REAL array, dimension (LDB, N)
</span><span class="comment">*</span><span class="comment">          On entry, the second of the pair of matrices.
</span><span class="comment">*</span><span class="comment">          On exit, B has been overwritten by its generalized Schur
</span><span class="comment">*</span><span class="comment">          form T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of B.  LDB &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SDIM    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          If SORT = 'N', SDIM = 0.
</span><span class="comment">*</span><span class="comment">          If SORT = 'S', SDIM = number of eigenvalues (after sorting)
</span><span class="comment">*</span><span class="comment">          for which SELCTG is true.  (Complex conjugate pairs for which
</span><span class="comment">*</span><span class="comment">          SELCTG is true for either eigenvalue count as 2.)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ALPHAR  (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">  ALPHAI  (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">  BETA    (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
</span><span class="comment">*</span><span class="comment">          be the generalized eigenvalues.  ALPHAR(j) + ALPHAI(j)*i,
</span><span class="comment">*</span><span class="comment">          and  BETA(j),j=1,...,N are the diagonals of the complex Schur
</span><span class="comment">*</span><span class="comment">          form (S,T) that would result if the 2-by-2 diagonal blocks of
</span><span class="comment">*</span><span class="comment">          the real Schur form of (A,B) were further reduced to
</span><span class="comment">*</span><span class="comment">          triangular form using 2-by-2 complex unitary transformations.
</span><span class="comment">*</span><span class="comment">          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
</span><span class="comment">*</span><span class="comment">          positive, then the j-th and (j+1)-st eigenvalues are a
</span><span class="comment">*</span><span class="comment">          complex conjugate pair, with ALPHAI(j+1) negative.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
</span><span class="comment">*</span><span class="comment">          may easily over- or underflow, and BETA(j) may even be zero.
</span><span class="comment">*</span><span class="comment">          Thus, the user should avoid naively computing the ratio.
</span><span class="comment">*</span><span class="comment">          However, ALPHAR and ALPHAI will be always less than and
</span><span class="comment">*</span><span class="comment">          usually comparable with norm(A) in magnitude, and BETA always
</span><span class="comment">*</span><span class="comment">          less than and usually comparable with norm(B).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VSL     (output) REAL array, dimension (LDVSL,N)
</span><span class="comment">*</span><span class="comment">          If JOBVSL = 'V', VSL will contain the left Schur vectors.
</span><span class="comment">*</span><span class="comment">          Not referenced if JOBVSL = 'N'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVSL   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix VSL. LDVSL &gt;=1, and
</span><span class="comment">*</span><span class="comment">          if JOBVSL = 'V', LDVSL &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VSR     (output) REAL array, dimension (LDVSR,N)
</span><span class="comment">*</span><span class="comment">          If JOBVSR = 'V', VSR will contain the right Schur vectors.
</span><span class="comment">*</span><span class="comment">          Not referenced if JOBVSR = 'N'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVSR   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix VSR. LDVSR &gt;= 1, and
</span><span class="comment">*</span><span class="comment">          if JOBVSR = 'V', LDVSR &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment">          If N = 0, LWORK &gt;= 1, else LWORK &gt;= max(8*N,6*N+16).
</span><span class="comment">*</span><span class="comment">          For good performance , LWORK must generally be larger.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.165"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  BWORK   (workspace) LOGICAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          Not referenced if SORT = 'N'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">          = 1,...,N:
</span><span class="comment">*</span><span class="comment">                The QZ iteration failed.  (A,B) are not in Schur
</span><span class="comment">*</span><span class="comment">                form, but ALPHAR(j), ALPHAI(j), and BETA(j) should
</span><span class="comment">*</span><span class="comment">                be correct for j=INFO+1,...,N.
</span><span class="comment">*</span><span class="comment">          &gt; N:  =N+1: other than QZ iteration failed in <a name="SHGEQZ.177"></a><a href="shgeqz.f.html#SHGEQZ.1">SHGEQZ</a>.
</span><span class="comment">*</span><span class="comment">                =N+2: after reordering, roundoff changed values of
</span><span class="comment">*</span><span class="comment">                      some complex eigenvalues so that leading
</span><span class="comment">*</span><span class="comment">                      eigenvalues in the Generalized Schur form no
</span><span class="comment">*</span><span class="comment">                      longer satisfy SELCTG=.TRUE.  This could also
</span><span class="comment">*</span><span class="comment">                      be caused due to scaling.
</span><span class="comment">*</span><span class="comment">                =N+3: reordering failed in <a name="STGSEN.183"></a><a href="stgsen.f.html#STGSEN.1">STGSEN</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
     $                   LQUERY, LST2SL, WANTST
      INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
     $                   ILO, IP, IRIGHT, IROWS, ITAU, IWRK, MAXWRK,
     $                   MINWRK
      REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
     $                   PVSR, SAFMAX, SAFMIN, SMLNUM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      INTEGER            IDUM( 1 )
      REAL               DIF( 2 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SGEQRF.205"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>, <a name="SGGBAK.205"></a><a href="sggbak.f.html#SGGBAK.1">SGGBAK</a>, <a name="SGGBAL.205"></a><a href="sggbal.f.html#SGGBAL.1">SGGBAL</a>, <a name="SGGHRD.205"></a><a href="sgghrd.f.html#SGGHRD.1">SGGHRD</a>, <a name="SHGEQZ.205"></a><a href="shgeqz.f.html#SHGEQZ.1">SHGEQZ</a>, <a name="SLABAD.205"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>,
     $                   <a name="SLACPY.206"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>, <a name="SLASCL.206"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>, <a name="SLASET.206"></a><a href="slaset.f.html#SLASET.1">SLASET</a>, <a name="SORGQR.206"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>, <a name="SORMQR.206"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>, <a name="STGSEN.206"></a><a href="stgsen.f.html#STGSEN.1">STGSEN</a>,
     $                   <a name="XERBLA.207"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.210"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.211"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
      REAL               <a name="SLAMCH.212"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.212"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
      EXTERNAL           <a name="LSAME.213"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.213"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>, <a name="SLAMCH.213"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.213"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Decode the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.222"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSL, <span class="string">'N'</span> ) ) THEN
         IJOBVL = 1
         ILVSL = .FALSE.
      ELSE IF( <a name="LSAME.225"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSL, <span class="string">'V'</span> ) ) THEN
         IJOBVL = 2
         ILVSL = .TRUE.
      ELSE
         IJOBVL = -1
         ILVSL = .FALSE.
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.233"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSR, <span class="string">'N'</span> ) ) THEN
         IJOBVR = 1
         ILVSR = .FALSE.
      ELSE IF( <a name="LSAME.236"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSR, <span class="string">'V'</span> ) ) THEN
         IJOBVR = 2
         ILVSR = .TRUE.
      ELSE
         IJOBVR = -1
         ILVSR = .FALSE.
      END IF
<span class="comment">*</span><span class="comment">
</span>      WANTST = <a name="LSAME.244"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'S'</span> )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      IF( IJOBVL.LE.0 ) THEN
         INFO = -1
      ELSE IF( IJOBVR.LE.0 ) THEN
         INFO = -2
      ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.<a name="LSAME.254"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'N'</span> ) ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -7
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -9
      ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
         INFO = -15
      ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
         INFO = -17
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute workspace
</span><span class="comment">*</span><span class="comment">      (Note: Comments in the code beginning &quot;Workspace:&quot; describe the
</span><span class="comment">*</span><span class="comment">       minimal amount of workspace needed at that point in the code,
</span><span class="comment">*</span><span class="comment">       as well as the preferred amount for good performance.
</span><span class="comment">*</span><span class="comment">       NB refers to the optimal block size for the immediately
</span><span class="comment">*</span><span class="comment">       following subroutine, as returned by <a name="ILAENV.273"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>.)
</span><span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         IF( N.GT.0 )THEN
            MINWRK = MAX( 8*N, 6*N + 16 )
            MAXWRK = MINWRK - N +
     $               N*<a name="ILAENV.279"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="SGEQRF.279"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>'</span>, <span class="string">' '</span>, N, 1, N, 0 )
            MAXWRK = MAX( MAXWRK, MINWRK - N +
     $                    N*<a name="ILAENV.281"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="SORMQR.281"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>'</span>, <span class="string">' '</span>, N, 1, N, -1 ) )
            IF( ILVSL ) THEN
               MAXWRK = MAX( MAXWRK, MINWRK - N +
     $                       N*<a name="ILAENV.284"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="SORGQR.284"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>'</span>, <span class="string">' '</span>, N, 1, N, -1 ) )
            END IF
         ELSE
            MINWRK = 1
            MAXWRK = 1
         END IF
         WORK( 1 ) = MAXWRK
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
     $      INFO = -19
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.297"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SGGES.297"></a><a href="sgges.f.html#SGGES.1">SGGES</a> '</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 ) THEN
         SDIM = 0
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Get machine constants
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="SLAMCH.312"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'P'</span> )
      SAFMIN = <a name="SLAMCH.313"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> )
      SAFMAX = ONE / SAFMIN
      CALL <a name="SLABAD.315"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>( SAFMIN, SAFMAX )
      SMLNUM = SQRT( SAFMIN ) / EPS
      BIGNUM = ONE / SMLNUM
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale A if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      ANRM = <a name="SLANGE.321"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'M'</span>, N, N, A, LDA, WORK )
      ILASCL = .FALSE.
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
         ANRMTO = SMLNUM
         ILASCL = .TRUE.
      ELSE IF( ANRM.GT.BIGNUM ) THEN
         ANRMTO = BIGNUM
         ILASCL = .TRUE.
      END IF
      IF( ILASCL )
     $   CALL <a name="SLASCL.331"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale B if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      BNRM = <a name="SLANGE.335"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'M'</span>, N, N, B, LDB, WORK )
      ILBSCL = .FALSE.
      IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
         BNRMTO = SMLNUM
         ILBSCL = .TRUE.
      ELSE IF( BNRM.GT.BIGNUM ) THEN
         BNRMTO = BIGNUM
         ILBSCL = .TRUE.
      END IF
      IF( ILBSCL )
     $   CALL <a name="SLASCL.345"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Permute the matrix to make it more nearly triangular
</span><span class="comment">*</span><span class="comment">     (Workspace: need 6*N + 2*N space for storing balancing factors)
</span><span class="comment">*</span><span class="comment">
</span>      ILEFT = 1
      IRIGHT = N + 1
      IWRK = IRIGHT + N
      CALL <a name="SGGBAL.353"></a><a href="sggbal.f.html#SGGBAL.1">SGGBAL</a>( <span class="string">'P'</span>, N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ),
     $             WORK( IRIGHT ), WORK( IWRK ), IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reduce B to triangular form (QR decomposition of B)
</span><span class="comment">*</span><span class="comment">     (Workspace: need N, prefer N*NB)
</span><span class="comment">*</span><span class="comment">
</span>      IROWS = IHI + 1 - ILO
      ICOLS = N + 1 - ILO
      ITAU = IWRK
      IWRK = ITAU + IROWS
      CALL <a name="SGEQRF.363"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
     $             WORK( IWRK ), LWORK+1-IWRK, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Apply the orthogonal transformation to matrix A
</span><span class="comment">*</span><span class="comment">     (Workspace: need N, prefer N*NB)
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SORMQR.369"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>( <span class="string">'L'</span>, <span class="string">'T'</span>, IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
     $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
     $             LWORK+1-IWRK, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initialize VSL
</span><span class="comment">*</span><span class="comment">     (Workspace: need N, prefer N*NB)
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILVSL ) THEN
         CALL <a name="SLASET.377"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'Full'</span>, N, N, ZERO, ONE, VSL, LDVSL )
         IF( IROWS.GT.1 ) THEN
            CALL <a name="SLACPY.379"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'L'</span>, IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
     $                   VSL( ILO+1, ILO ), LDVSL )
         END IF
         CALL <a name="SORGQR.382"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
     $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initialize VSR
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILVSR )
     $   CALL <a name="SLASET.389"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'Full'</span>, N, N, ZERO, ONE, VSR, LDVSR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reduce to generalized Hessenberg form
</span><span class="comment">*</span><span class="comment">     (Workspace: none needed)
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SGGHRD.394"></a><a href="sgghrd.f.html#SGGHRD.1">SGGHRD</a>( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
     $             LDVSL, VSR, LDVSR, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Perform QZ algorithm, computing Schur vectors if desired
</span><span class="comment">*</span><span class="comment">     (Workspace: need N)
</span><span class="comment">*</span><span class="comment">
</span>      IWRK = ITAU
      CALL <a name="SHGEQZ.401"></a><a href="shgeqz.f.html#SHGEQZ.1">SHGEQZ</a>( <span class="string">'S'</span>, JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
     $             ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
     $             WORK( IWRK ), LWORK+1-IWRK, IERR )
      IF( IERR.NE.0 ) THEN
         IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
            INFO = IERR
         ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
            INFO = IERR - N
         ELSE
            INFO = N + 1
         END IF
         GO TO 40
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Sort eigenvalues ALPHA/BETA if desired
</span><span class="comment">*</span><span class="comment">     (Workspace: need 4*N+16 )
</span><span class="comment">*</span><span class="comment">
</span>      SDIM = 0
      IF( WANTST ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Undo scaling on eigenvalues before SELCTGing
</span><span class="comment">*</span><span class="comment">
</span>         IF( ILASCL ) THEN
            CALL <a name="SLASCL.424"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N,
     $                   IERR )
            CALL <a name="SLASCL.426"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N,
     $                   IERR )
         END IF
         IF( ILBSCL )
     $      CALL <a name="SLASCL.430"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Select eigenvalues
</span><span class="comment">*</span><span class="comment">
</span>         DO 10 I = 1, N
            BWORK( I ) = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
   10    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         CALL <a name="STGSEN.438"></a><a href="stgsen.f.html#STGSEN.1">STGSEN</a>( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHAR,
     $                ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL,
     $                PVSR, DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1,
     $                IERR )
         IF( IERR.EQ.1 )
     $      INFO = N + 3
<span class="comment">*</span><span class="comment">
</span>      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Apply back-permutation to VSL and VSR
</span><span class="comment">*</span><span class="comment">     (Workspace: none needed)
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILVSL )
     $   CALL <a name="SGGBAK.451"></a><a href="sggbak.f.html#SGGBAK.1">SGGBAK</a>( <span class="string">'P'</span>, <span class="string">'L'</span>, N, ILO, IHI, WORK( ILEFT ),
     $                WORK( IRIGHT ), N, VSL, LDVSL, IERR )
<span class="comment">*</span><span class="comment">
</span>      IF( ILVSR )
     $   CALL <a name="SGGBAK.455"></a><a href="sggbak.f.html#SGGBAK.1">SGGBAK</a>( <span class="string">'P'</span>, <span class="string">'R'</span>, N, ILO, IHI, WORK( ILEFT ),
     $                WORK( IRIGHT ), N, VSR, LDVSR, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check if unscaling would cause over/underflow, if so, rescale 
</span><span class="comment">*</span><span class="comment">     (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of 
</span><span class="comment">*</span><span class="comment">     B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I)
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILASCL )THEN
         DO 50 I = 1, N 
            IF( ALPHAI( I ).NE.ZERO ) THEN 
               IF( ( ALPHAR( I )/SAFMAX ).GT.( ANRMTO/ANRM ) .OR.
     $             ( SAFMIN/ALPHAR( I ) ).GT.( ANRM/ANRMTO ) ) THEN
                  WORK( 1 ) = ABS( A( I, I )/ALPHAR( I ) )
                  BETA( I ) = BETA( I )*WORK( 1 )
                  ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                  ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
               ELSE IF( ( ALPHAI( I )/SAFMAX ).GT.( ANRMTO/ANRM ) .OR.
     $             ( SAFMIN/ALPHAI( I ) ).GT.( ANRM/ANRMTO ) ) THEN
                  WORK( 1 ) = ABS( A( I, I+1 )/ALPHAI( I ) )
                  BETA( I ) = BETA( I )*WORK( 1 )
                  ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                  ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
               END IF
            END IF
   50    CONTINUE
      END IF 
<span class="comment">*</span><span class="comment">
</span>      IF( ILBSCL )THEN 
         DO 60 I = 1, N
            IF( ALPHAI( I ).NE.ZERO ) THEN
                IF( ( BETA( I )/SAFMAX ).GT.( BNRMTO/BNRM ) .OR.
     $              ( SAFMIN/BETA( I ) ).GT.( BNRM/BNRMTO ) ) THEN
                   WORK( 1 ) = ABS(B( I, I )/BETA( I ))
                   BETA( I ) = BETA( I )*WORK( 1 )
                   ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                   ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
                END IF 
             END IF
   60    CONTINUE 
      END IF 
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Undo scaling
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILASCL ) THEN
         CALL <a name="SLASCL.499"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'H'</span>, 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
         CALL <a name="SLASCL.500"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR )
         CALL <a name="SLASCL.501"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR )
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( ILBSCL ) THEN
         CALL <a name="SLASCL.505"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'U'</span>, 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
         CALL <a name="SLASCL.506"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( WANTST ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Check if reordering is correct
</span><span class="comment">*</span><span class="comment">
</span>         LASTSL = .TRUE.
         LST2SL = .TRUE.
         SDIM = 0
         IP = 0
         DO 30 I = 1, N
            CURSL = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
            IF( ALPHAI( I ).EQ.ZERO ) THEN
               IF( CURSL )
     $            SDIM = SDIM + 1
               IP = 0
               IF( CURSL .AND. .NOT.LASTSL )
     $            INFO = N + 2
            ELSE
               IF( IP.EQ.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Last eigenvalue of conjugate pair
</span><span class="comment">*</span><span class="comment">
</span>                  CURSL = CURSL .OR. LASTSL
                  LASTSL = CURSL
                  IF( CURSL )
     $               SDIM = SDIM + 2
                  IP = -1
                  IF( CURSL .AND. .NOT.LST2SL )
     $               INFO = N + 2
               ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 First eigenvalue of conjugate pair
</span><span class="comment">*</span><span class="comment">
</span>                  IP = 1
               END IF
            END IF
            LST2SL = LASTSL
            LASTSL = CURSL
   30    CONTINUE
<span class="comment">*</span><span class="comment">
</span>      END IF
<span class="comment">*</span><span class="comment">
</span>   40 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      WORK( 1 ) = MAXWRK
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SGGES.556"></a><a href="sgges.f.html#SGGES.1">SGGES</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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